Towards numerical implementation of the relativistically covariant many-body perturbation theoryThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

2009 ◽  
Vol 87 (7) ◽  
pp. 817-824 ◽  
Author(s):  
Daniel Hedendahl ◽  
Ingvar Lindgren ◽  
Sten Salomonson
Keyword(s):  
Standard Procedure ◽  
Operator Method ◽  
Vertex Correction ◽  
Many Body ◽  
Atomic Systems ◽  
Self Energy ◽  
Electron Positron ◽  
Many Body Perturbation Theory ◽  
Qed Effects ◽  
First Time

The standard procedure for relativistic many-body perturbation theory (RMBPT) is not relativistically covariant, and the effects of retardation, virtual-electron-positron-pair, and radiative effects (self-energy, vacuum polarisation, and vertex correction) — the so-called QED effects — are left out. The energy contribution from the QED effects can be evaluated by the covariant evolution operator method, which has a structure that is similar to that of RMBPT, and it can serve as a merger between QED and RMBPT. The new procedure makes it, in principle, possible for the first time to evaluate QED effects together with correlation to high order. The procedure is now being implemented, and it has been shown that the effect of electron correlation on first-order QED for He-like neon dominates heavily over second-order QED effects.

scholarly journals Design of auxiliary systems for spectroscopy

2020 ◽  
Vol 224 ◽  
pp. 424-447
Author(s):  
Marco Vanzini ◽  
Francesco Sottile ◽  
Igor Reshetnyak ◽  
Sergio Ciuchi ◽  
Lucia Reining ◽  
...  
Keyword(s):  
Spectral Properties ◽  
Density Functional ◽  
The Self ◽  
Many Body ◽  
Functional Theory ◽  
Correlation Kernel ◽  
Effective Potentials ◽  
Exchange Correlation ◽  
Self Energy ◽  
Many Body Perturbation Theory

In this contribution, we advocate the possibility of designing auxiliary systems with effective potentials or kernels that target only the specific spectral properties of interest and are simpler than the self-energy of many-body perturbation theory or the exchange–correlation kernel of time-dependent density-functional theory.

THE SCREENING FUNCTION OF AN INTERACTING ELECTRON GAS

1966 ◽  
Vol 44 (9) ◽  
pp. 2137-2171 ◽  
Author(s):  
D. J. W. Geldart ◽  
S. H. Vosko
Keyword(s):  
Electron Gas ◽  
Substantial Contribution ◽  
Fundamental Relation ◽  
Many Body ◽  
Screening Constant ◽  
Self Energy ◽  
Self Consistent ◽  
Small Wave ◽  
Many Body Perturbation Theory ◽  
Zero Frequency

The screening function of an interacting electron gas at high and metallic densities is investigated by many-body perturbation theory. The analysis is guided by a fundamental relation between the compressibility of the system and the zero-frequency small wave-vector screening function (i.e. screening constant). It is shown that the contribution from a graph not included in previous work is essential to obtain the lowest-order correlation correction to the screening constant at high density. Also, this graph gives a substantial contribution to the screening constant at metallic densities. The general problem of choosing a self-consistent set of graphs for calculating the screening function is discussed in terms of a coupled set of integral equations for the propagator, the self-energy, the vertex function, and the screening function. A modification of Hubbard's (1957) form of the screening function is put forward on the basis of these results.

NON-FRANCK–CONDON EFFECTS IN THE PHOTOIONIZATION OF N2 TO THE ${\rm N}_2^+$ A 2Πu STATE AND OF O2 TO THE ${\rm O}_2^+$ X 2Πg STATE IN THE 19–34 eV PHOTON ENERGY REGION

2002 ◽  
Vol 09 (01) ◽  
pp. 147-152
Author(s):  
J. RIUS I RIU ◽  
J. ÁLVAREZ ◽  
A. KARAWAJCZYK ◽  
M. STANKIEWICZ ◽  
P. WINIARCZYK ◽  
...  
Keyword(s):  
Cross Sections ◽  
Photoelectron Spectroscopy ◽  
Branching Ratios ◽  
Rydberg Series ◽  
Many Body ◽  
Channel Coupling ◽  
Valence States ◽  
Many Body Perturbation Theory ◽  
First Time ◽  
Franck Condon

Photoionization to the [Formula: see text] A 2Πu state and to the [Formula: see text] X 2Πg state is studied using photoelectron spectroscopy. The experimental vibrational branching ratios are obtained for the first time in the 19–34 eV region for the v′ = 0–3 levels, for both molecules. Ab initio many-body perturbation theory is used to calculate branching ratios for ionization to the [Formula: see text] A 2Πu state and branching ratios, vibrationally resolved partial cross sections and total cross section for ionization to the [Formula: see text] X 2Πg state. The Franck–Condon breakdown observed in the photoionization of the N 2 1πu electron is mainly explained by autoionization from Rydberg and valence states of N 2, whereas photoionization of the O 2πg electron is not fully explained either by channel coupling effects or by autoionization from known Rydberg series and valence states.

Influence of Electron-Electron Correlations and Lattice Effects on Positron-Electron Enhancement Factors

2010 ◽  
Vol 666 ◽  
pp. 5-9 ◽  
Author(s):  
Edward Boroński
Keyword(s):  
Electron Gas ◽  
Momentum Density ◽  
Many Body ◽  
Fermi Sphere ◽  
Self Energy ◽  
Density Distributions ◽  
Lattice Effects ◽  
Electron Positron ◽  
Enhancement Factors ◽  
Momentum Distributions

We present an approach taking into account the effect of electron-electron (e-e) correlations on electron-positron (e-p) momentum density distributions. The approach bases on the modification of the Bethe-Goldstone (B-G) equation for the positron in the electron gas due to self-energy effects. The example calculations have been performed for selected parameters corresponding to simple metals. The calculated dependencies exhibit the increase of the e-p enhancement factors below Fermi momentum, like Kahana enhancements, and a decrease above the Fermi sphere, leading to a many-body “tail” in the e-p momentum density distributions. Moreover, the influence of lattice effects on enhancement factors (EF) is taken into account. This decreases by a few percent the absolute values of the e-p momentum distributions and the corresponding annihilation rates and for real metals such as Mg or Cu evidently improve the agreement with experiment.

ENERGY-DEPENDENT MANY-BODY PERTURBATION THEORY: A ROAD TOWARDS A MANY-BODY-QED PROCEDURE

2007 ◽  
Vol 16 (04) ◽  
pp. 1221-1231 ◽  
Author(s):  
INGVAR LINDGREN ◽  
STEN SALOMONSON ◽  
DANIEL HEDENDAHL
Keyword(s):  
Perturbation Theory ◽  
Electron Correlation ◽  
Numerical Evaluation ◽  
Arbitrary Order ◽  
Coulomb Interactions ◽  
Many Body ◽  
Many Body Perturbation Theory ◽  
Qed Effects ◽  
Energy Dependent ◽  
Rigorous Procedure

A rigorous procedure for energy-dependent many-body perturbation theory (MBPT) is presented. This can be applied for numerical evaluation of many-body-QED effects by combining QED with electron correlation to arbitrary order. So far, it has been used only for the exchange of a single retarded photon together with an arbitrary number of instantaneous Coulomb interactions. For heliumlike neon this represents more than 99% of the nonradiative effect on the energy beyond standard MBPT.

scholarly journals Parity non-conservation effect in heavy atomic systems within relativistic many-body perturbation theory: Advanced data

2019 ◽  
Vol 1289 ◽  
pp. 012025
Author(s):  
O Yu Khetselius ◽  
V B Ternovsky ◽  
A A Svinarenko ◽  
Yu V Dubrovskaya ◽  
I N Serga
Keyword(s):  
Perturbation Theory ◽  
Many Body ◽  
Atomic Systems ◽  
Many Body Perturbation Theory

scholarly journals Many-Electron QED with Redefined Vacuum Approach

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1014
Author(s):  
Romain N. Soguel ◽  
Andrey V. Volotka ◽  
Dmitry A. Glazov ◽  
Stephan Fritzsche
Keyword(s):  
Perturbation Theory ◽  
Electronic Configuration ◽  
Bound State ◽  
Many Body ◽  
Photon Exchange ◽  
Self Energy ◽  
Many Body Perturbation Theory ◽  
Formula Derivation ◽  
The Many ◽  
The One

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

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